Blinking cursor in Firefox 2 bleeds through divs...

I have a weird problem I'm running into again, but haven't been able to find a fix. In FF2, when I place a <div /> over an <input /> element that currently has focus, the blinking cursor shows up through the top layer.

I put together this little video to show off the problem:

Here's a working example of the bug. If you open the page in Firefox 2, you should see the cursor blinking in the middle of the word overlay.